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Paradoxes of Mathematical Space

Dr Richard Earl, Worcester College, University of Oxford

Date Icon Week 1, Tuesday 24 April TT 2012
Time Icon 8:15pm

Through the 19th century and into the 20th, mathematicians began increasingly to uncover surprises (some nice, some nasty) amongst their notions of geometry and space. Seemingly axiomatic ideas like the parallel postulate, crucial notions such dimension and volume were, all of a sudden, much less certain than had been previously been the case. This talk covers some of those seminal discoveries with a focus mainly on the Banach-Tarski paradox which states that, by means of breaking an object into finitely many pieces, its volume can be doubled; reassuringly (or perhaps not!) this is not the case with area.